Question: $83$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $112$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 83}$ ${x = 4y-112}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-112}$ for $x$ in the first equation. ${(4y-112)}{+ y = 83}$ Simplify and solve for $y$ $ 4y-112 + y = 83 $ $ 5y-112 = 83 $ $ 5y = 195 $ $ y = \dfrac{195}{5} $ ${y = 39}$ Now that you know ${y = 39}$ , plug it back into ${x = 4y-112}$ to find $x$ ${x = 4}{(39)}{ - 112}$ $x = 156 - 112$ ${x = 44}$ You can also plug ${y = 39}$ into ${x+y = 83}$ and get the same answer for $x$ ${x + }{(39)}{= 83}$ ${x = 44}$ There were $44$ home team fans and $39$ away team fans.